/*
 * jidctfst.c
 *
 * Copyright (C) 1994-1995, Thomas G. Lane.
 * This file is part of the Independent JPEG Group's software.
 * For conditions of distribution and use, see the accompanying README file.
 *
 * This file contains a fast, not so accurate integer implementation of the
 * inverse DCT (Discrete Cosine Transform).  In the IJG code, this routine
 * must also perform dequantization of the input coefficients.
 *
 * A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT
 * on each row (or vice versa, but it's more convenient to emit a row at
 * a time).  Direct algorithms are also available, but they are much more
 * complex and seem not to be any faster when reduced to code.
 *
 * This implementation is based on Arai, Agui, and Nakajima's algorithm for
 * scaled DCT.  Their original paper (Trans. IEICE E-71(11):1095) is in
 * Japanese, but the algorithm is described in the Pennebaker & Mitchell
 * JPEG textbook (see REFERENCES section in file README).  The following code
 * is based directly on figure 4-8 in P&M.
 * While an 8-point DCT cannot be done in less than 11 multiplies, it is
 * possible to arrange the computation so that many of the multiplies are
 * simple scalings of the final outputs.  These multiplies can then be
 * folded into the multiplications or divisions by the JPEG quantization
 * table entries.  The AA&N method leaves only 5 multiplies and 29 adds
 * to be done in the DCT itself.
 * The primary disadvantage of this method is that with fixed-point math,
 * accuracy is lost due to imprecise representation of the scaled
 * quantization values.  The smaller the quantization table entry, the less
 * precise the scaled value, so this implementation does worse with high-
 * quality-setting files than with low-quality ones.
 */

#define JPEG_INTERNALS
#include "jinclude.h"
#include "jpeglib.h"
#include "jdct.h"        /* Private declarations for DCT subsystem */

#ifdef DCT_IFAST_SUPPORTED


/*
 * This module is specialized to the case DCTSIZE = 8.
 */

#if DCTSIZE != 8
Sorry, this code only copes with 8 x8 DCTs.  /* deliberate syntax err */
    #endif


/* Scaling decisions are generally the same as in the LL&M algorithm;
 * see jidctint.c for more details.  However, we choose to descale
 * (right shift) multiplication products as soon as they are formed,
 * rather than carrying additional fractional bits into subsequent additions.
 * This compromises accuracy slightly, but it lets us save a few shifts.
 * More importantly, 16-bit arithmetic is then adequate (for 8-bit samples)
 * everywhere except in the multiplications proper; this saves a good deal
 * of work on 16-bit-int machines.
 *
 * The dequantized coefficients are not integers because the AA&N scaling
 * factors have been incorporated.  We represent them scaled up by PASS1_BITS,
 * so that the first and second IDCT rounds have the same input scaling.
 * For 8-bit JSAMPLEs, we choose IFAST_SCALE_BITS = PASS1_BITS so as to
 * avoid a descaling shift; this compromises accuracy rather drastically
 * for small quantization table entries, but it saves a lot of shifts.
 * For 12-bit JSAMPLEs, there's no hope of using 16x16 multiplies anyway,
 * so we use a much larger scaling factor to preserve accuracy.
 *
 * A final compromise is to represent the multiplicative constants to only
 * 8 fractional bits, rather than 13.  This saves some shifting work on some
 * machines, and may also reduce the cost of multiplication (since there
 * are fewer one-bits in the constants).
 */

#if BITS_IN_JSAMPLE == 8
#define CONST_BITS  8
#define PASS1_BITS  2
#else
#define CONST_BITS  8
#define PASS1_BITS  1       /* lose a little precision to avoid overflow */
#endif

/* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
 * causing a lot of useless floating-point operations at run time.
 * To get around this we use the following pre-calculated constants.
 * If you change CONST_BITS you may want to add appropriate values.
 * (With a reasonable C compiler, you can just rely on the FIX() macro...)
 */

#if CONST_BITS == 8
#define FIX_1_082392200  ( (INT32)  277 )     /* FIX(1.082392200) */
#define FIX_1_414213562  ( (INT32)  362 )     /* FIX(1.414213562) */
#define FIX_1_847759065  ( (INT32)  473 )     /* FIX(1.847759065) */
#define FIX_2_613125930  ( (INT32)  669 )     /* FIX(2.613125930) */
#else
#define FIX_1_082392200  FIX( 1.082392200 )
#define FIX_1_414213562  FIX( 1.414213562 )
#define FIX_1_847759065  FIX( 1.847759065 )
#define FIX_2_613125930  FIX( 2.613125930 )
#endif


/* We can gain a little more speed, with a further compromise in accuracy,
 * by omitting the addition in a descaling shift.  This yields an incorrectly
 * rounded result half the time...
 */

#ifndef USE_ACCURATE_ROUNDING
#undef DESCALE
#define DESCALE( x, n )  RIGHT_SHIFT( x, n )
#endif


/* Multiply a DCTELEM variable by an INT32 constant, and immediately
 * descale to yield a DCTELEM result.
 */

#define MULTIPLY( var, const )  ( (DCTELEM) DESCALE( ( var ) * ( const ), CONST_BITS ) )


/* Dequantize a coefficient by multiplying it by the multiplier-table
 * entry; produce a DCTELEM result.  For 8-bit data a 16x16->16
 * multiplication will do.  For 12-bit data, the multiplier table is
 * declared INT32, so a 32-bit multiply will be used.
 */

#if BITS_IN_JSAMPLE == 8
#define DEQUANTIZE( coef, quantval )  ( ( (IFAST_MULT_TYPE) ( coef ) ) * ( quantval ) )
#else
#define DEQUANTIZE( coef, quantval )  \
    DESCALE( ( coef ) * ( quantval ), IFAST_SCALE_BITS - PASS1_BITS )
#endif


/* Like DESCALE, but applies to a DCTELEM and produces an int.
 * We assume that int right shift is unsigned if INT32 right shift is.
 */

#ifdef RIGHT_SHIFT_IS_UNSIGNED
#define ISHIFT_TEMPS    DCTELEM ishift_temp;
#if BITS_IN_JSAMPLE == 8
#define DCTELEMBITS  16     /* DCTELEM may be 16 or 32 bits */
#else
#define DCTELEMBITS  32     /* DCTELEM must be 32 bits */
#endif
#define IRIGHT_SHIFT( x, shft )  \
    ( ( ishift_temp = ( x ) ) < 0 ? \
                      ( ishift_temp >> ( shft ) ) | ( ( ~( (DCTELEM) 0 ) ) << ( DCTELEMBITS - ( shft ) ) ) : \
                      ( ishift_temp >> ( shft ) ) )
#else
#define ISHIFT_TEMPS
#define IRIGHT_SHIFT( x, shft )    ( ( x ) >> ( shft ) )
#endif

#ifdef USE_ACCURATE_ROUNDING
#define IDESCALE( x, n )  ( (int) IRIGHT_SHIFT( ( x ) + ( 1 << ( ( n ) - 1 ) ), n ) )
#else
#define IDESCALE( x, n )  ( (int) IRIGHT_SHIFT( x, n ) )
#endif


/*
 * Perform dequantization and inverse DCT on one block of coefficients.
 */

GLOBAL void
jpeg_idct_ifast( j_decompress_ptr cinfo, jpeg_component_info * compptr,
                 JCOEFPTR coef_block,
                 JSAMPARRAY output_buf, JDIMENSION output_col ) {
    DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
    DCTELEM tmp10, tmp11, tmp12, tmp13;
    DCTELEM z5, z10, z11, z12, z13;
    JCOEFPTR inptr;
    IFAST_MULT_TYPE * quantptr;
    int * wsptr;
    JSAMPROW outptr;
    JSAMPLE * range_limit = IDCT_range_limit( cinfo );
    int ctr;
    int workspace[DCTSIZE2];/* buffers data between passes */
    SHIFT_TEMPS         /* for DESCALE */
    ISHIFT_TEMPS        /* for IDESCALE */

    /* Pass 1: process columns from input, store into work array. */

    inptr = coef_block;
    quantptr = (IFAST_MULT_TYPE *) compptr->dct_table;
    wsptr = workspace;
    for ( ctr = DCTSIZE; ctr > 0; ctr-- ) {
        /* Due to quantization, we will usually find that many of the input
         * coefficients are zero, especially the AC terms.  We can exploit this
         * by short-circuiting the IDCT calculation for any column in which all
         * the AC terms are zero.  In that case each output is equal to the
         * DC coefficient (with scale factor as needed).
         * With typical images and quantization tables, half or more of the
         * column DCT calculations can be simplified this way.
         */

        if ( ( inptr[DCTSIZE * 1] | inptr[DCTSIZE * 2] | inptr[DCTSIZE * 3] |
               inptr[DCTSIZE * 4] | inptr[DCTSIZE * 5] | inptr[DCTSIZE * 6] |
               inptr[DCTSIZE * 7] ) == 0 ) {
            /* AC terms all zero */
            int dcval = (int) DEQUANTIZE( inptr[DCTSIZE * 0], quantptr[DCTSIZE * 0] );

            wsptr[DCTSIZE * 0] = dcval;
            wsptr[DCTSIZE * 1] = dcval;
            wsptr[DCTSIZE * 2] = dcval;
            wsptr[DCTSIZE * 3] = dcval;
            wsptr[DCTSIZE * 4] = dcval;
            wsptr[DCTSIZE * 5] = dcval;
            wsptr[DCTSIZE * 6] = dcval;
            wsptr[DCTSIZE * 7] = dcval;

            inptr++;    /* advance pointers to next column */
            quantptr++;
            wsptr++;
            continue;
        }

        /* Even part */

        tmp0 = DEQUANTIZE( inptr[DCTSIZE * 0], quantptr[DCTSIZE * 0] );
        tmp1 = DEQUANTIZE( inptr[DCTSIZE * 2], quantptr[DCTSIZE * 2] );
        tmp2 = DEQUANTIZE( inptr[DCTSIZE * 4], quantptr[DCTSIZE * 4] );
        tmp3 = DEQUANTIZE( inptr[DCTSIZE * 6], quantptr[DCTSIZE * 6] );

        tmp10 = tmp0 + tmp2;/* phase 3 */
        tmp11 = tmp0 - tmp2;

        tmp13 = tmp1 + tmp3;/* phases 5-3 */
        tmp12 = MULTIPLY( tmp1 - tmp3, FIX_1_414213562 ) - tmp13;/* 2*c4 */

        tmp0 = tmp10 + tmp13;/* phase 2 */
        tmp3 = tmp10 - tmp13;
        tmp1 = tmp11 + tmp12;
        tmp2 = tmp11 - tmp12;

        /* Odd part */

        tmp4 = DEQUANTIZE( inptr[DCTSIZE * 1], quantptr[DCTSIZE * 1] );
        tmp5 = DEQUANTIZE( inptr[DCTSIZE * 3], quantptr[DCTSIZE * 3] );
        tmp6 = DEQUANTIZE( inptr[DCTSIZE * 5], quantptr[DCTSIZE * 5] );
        tmp7 = DEQUANTIZE( inptr[DCTSIZE * 7], quantptr[DCTSIZE * 7] );

        z13 = tmp6 + tmp5;  /* phase 6 */
        z10 = tmp6 - tmp5;
        z11 = tmp4 + tmp7;
        z12 = tmp4 - tmp7;

        tmp7 = z11 + z13;   /* phase 5 */
        tmp11 = MULTIPLY( z11 - z13, FIX_1_414213562 );/* 2*c4 */

        z5 = MULTIPLY( z10 + z12, FIX_1_847759065 );/* 2*c2 */
        tmp10 = MULTIPLY( z12, FIX_1_082392200 ) - z5;/* 2*(c2-c6) */
        tmp12 = MULTIPLY( z10, -FIX_2_613125930 ) + z5;/* -2*(c2+c6) */

        tmp6 = tmp12 - tmp7;/* phase 2 */
        tmp5 = tmp11 - tmp6;
        tmp4 = tmp10 + tmp5;

        wsptr[DCTSIZE * 0] = (int) ( tmp0 + tmp7 );
        wsptr[DCTSIZE * 7] = (int) ( tmp0 - tmp7 );
        wsptr[DCTSIZE * 1] = (int) ( tmp1 + tmp6 );
        wsptr[DCTSIZE * 6] = (int) ( tmp1 - tmp6 );
        wsptr[DCTSIZE * 2] = (int) ( tmp2 + tmp5 );
        wsptr[DCTSIZE * 5] = (int) ( tmp2 - tmp5 );
        wsptr[DCTSIZE * 4] = (int) ( tmp3 + tmp4 );
        wsptr[DCTSIZE * 3] = (int) ( tmp3 - tmp4 );

        inptr++;        /* advance pointers to next column */
        quantptr++;
        wsptr++;
    }

    /* Pass 2: process rows from work array, store into output array. */
    /* Note that we must descale the results by a factor of 8 == 2**3, */
    /* and also undo the PASS1_BITS scaling. */

    wsptr = workspace;
    for ( ctr = 0; ctr < DCTSIZE; ctr++ ) {
        outptr = output_buf[ctr] + output_col;
        /* Rows of zeroes can be exploited in the same way as we did with columns.
         * However, the column calculation has created many nonzero AC terms, so
         * the simplification applies less often (typically 5% to 10% of the time).
         * On machines with very fast multiplication, it's possible that the
         * test takes more time than it's worth.  In that case this section
         * may be commented out.
         */

#ifndef NO_ZERO_ROW_TEST
        if ( ( wsptr[1] | wsptr[2] | wsptr[3] | wsptr[4] | wsptr[5] | wsptr[6] |
               wsptr[7] ) == 0 ) {
            /* AC terms all zero */
            JSAMPLE dcval = range_limit[IDESCALE( wsptr[0], PASS1_BITS + 3 )
                                        & RANGE_MASK];

            outptr[0] = dcval;
            outptr[1] = dcval;
            outptr[2] = dcval;
            outptr[3] = dcval;
            outptr[4] = dcval;
            outptr[5] = dcval;
            outptr[6] = dcval;
            outptr[7] = dcval;

            wsptr += DCTSIZE;/* advance pointer to next row */
            continue;
        }
#endif

        /* Even part */

        tmp10 = ( (DCTELEM) wsptr[0] + (DCTELEM) wsptr[4] );
        tmp11 = ( (DCTELEM) wsptr[0] - (DCTELEM) wsptr[4] );

        tmp13 = ( (DCTELEM) wsptr[2] + (DCTELEM) wsptr[6] );
        tmp12 = MULTIPLY( (DCTELEM) wsptr[2] - (DCTELEM) wsptr[6], FIX_1_414213562 )
                - tmp13;

        tmp0 = tmp10 + tmp13;
        tmp3 = tmp10 - tmp13;
        tmp1 = tmp11 + tmp12;
        tmp2 = tmp11 - tmp12;

        /* Odd part */

        z13 = (DCTELEM) wsptr[5] + (DCTELEM) wsptr[3];
        z10 = (DCTELEM) wsptr[5] - (DCTELEM) wsptr[3];
        z11 = (DCTELEM) wsptr[1] + (DCTELEM) wsptr[7];
        z12 = (DCTELEM) wsptr[1] - (DCTELEM) wsptr[7];

        tmp7 = z11 + z13;   /* phase 5 */
        tmp11 = MULTIPLY( z11 - z13, FIX_1_414213562 );/* 2*c4 */

        z5 = MULTIPLY( z10 + z12, FIX_1_847759065 );/* 2*c2 */
        tmp10 = MULTIPLY( z12, FIX_1_082392200 ) - z5;/* 2*(c2-c6) */
        tmp12 = MULTIPLY( z10, -FIX_2_613125930 ) + z5;/* -2*(c2+c6) */

        tmp6 = tmp12 - tmp7;/* phase 2 */
        tmp5 = tmp11 - tmp6;
        tmp4 = tmp10 + tmp5;

        /* Final output stage: scale down by a factor of 8 and range-limit */

        outptr[0] = range_limit[IDESCALE( tmp0 + tmp7, PASS1_BITS + 3 )
                                & RANGE_MASK];
        outptr[7] = range_limit[IDESCALE( tmp0 - tmp7, PASS1_BITS + 3 )
                                & RANGE_MASK];
        outptr[1] = range_limit[IDESCALE( tmp1 + tmp6, PASS1_BITS + 3 )
                                & RANGE_MASK];
        outptr[6] = range_limit[IDESCALE( tmp1 - tmp6, PASS1_BITS + 3 )
                                & RANGE_MASK];
        outptr[2] = range_limit[IDESCALE( tmp2 + tmp5, PASS1_BITS + 3 )
                                & RANGE_MASK];
        outptr[5] = range_limit[IDESCALE( tmp2 - tmp5, PASS1_BITS + 3 )
                                & RANGE_MASK];
        outptr[4] = range_limit[IDESCALE( tmp3 + tmp4, PASS1_BITS + 3 )
                                & RANGE_MASK];
        outptr[3] = range_limit[IDESCALE( tmp3 - tmp4, PASS1_BITS + 3 )
                                & RANGE_MASK];

        wsptr += DCTSIZE;   /* advance pointer to next row */
    }
}

#endif /* DCT_IFAST_SUPPORTED */
